Question

In a cricket match, a batswoman hits a boundary 6 times out of 30 balls she plays. Find the probability that she did not hit a boundary.

Answer 1

Hint: Sum of the probability of an event and its complementary event is equal to one. The probability of an event is defined as the ratio of the number of favourable cases to the total number of cases. Use the formula for finding the probability of an event i.e. $ {\text{Probability = }}\dfrac{{{\text{Number of favorable cases}}}}{{{\text{Total number of cases}}}} $

Complete step-by-step answer:
Probability gives us an estimate of how likely an event can occur. The probability cannot be negative or greater than 1.
Probability of any event lies between \[0 < P < 1\], where $ P $ is the numerical value of probability.
When the probability of an event is zero, it states that the event is impossible to occur.
When the probability of event is 1, it states that the event is certain to occur.
This concept of probability has been used in various fields such as gambling, data science, machine learning, engineering, physics, mathematics, finance, operation research, etc.
Let $ p $ and $ q $ be the probability of success and failure in hitting a boundary.
The events of success and failure in hitting a boundary are complementary to each other.
Hence, the sum of the probabilities of the success and failure will be equal to 1.
 $ p + q = 1......\left( 1 \right) $
We know that,
$\Rightarrow {\text{Probability = }}\dfrac{{{\text{Number of favourable cases}}}}{{{\text{Total number of cases}}}} $
When a batswoman hits 6 boundaries out of 30 balls, the probability of success can be given by $ p = \dfrac{6}{{30}} $ .
Substitute the value of $ p $ in the equation (1) to find the value of $ q $ .
When a batswoman isn’t able to hit boundaries, the probability of failure can be given by
\[
\Rightarrow p + q = 1\\
q = 1 - p\\
q = 1 - \dfrac{6}{{30}}\\
q = \dfrac{{30 - 6}}{{30}}
\]
\[\therefore q = \dfrac{{24}}{{30}}\]
After dividing the numerator and denominator by 6, we get, $ q = \dfrac{4}{5} $
Therefore, the probability that she did not hit a boundary is given by $ \dfrac{4}{5} $ .

Note: In this type of question, understanding the language of question is very important. Students should understand and analyse the information before using it in the formula. Apply the given condition to find the number of favourable cases.